My GPU makes a loud noise only when I use Eevee
My guess is that you get to very high temperatures while working with EEVEE. This results in coolers working more intensely. I believe - I had a similar problem - one of the coolers might not be in a correct position. This way he touches parts of the plastic it is embedded in. 
What you could do yourself on your own risk: Grab an app that shows the temperature and the coolers (Like this one). Look if what I said above is true (Temperature goes up, cooling needs be turned up). You can even try the Powermax app from the link I posted. This tests your cpu/gpu coolers rpm at different loads. If you go to high load you know that my theory is true. 
Open the PC and take a look at the coolers. All the coolers, also cpu. Try to get the right cooler in its place. Do it carefully. Try different angles. Or take the pc to the closest shop. It's your call  ;)

Hope it helped. Had a similar issue once.